Question

expand the expression to a polynomial in standard form
(x-9)(x^2+x+2)
you made me get the other question wrong so dont make me fail

Answer 1

To expand the expression \((x - 9)(x^2 + x + 2)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(x\) to each term in \(x^2 + x + 2\):
\[
x \cdot x^2 = x^3
\]
\[
x \cdot x = x^2
\]
\[
x \cdot 2 = 2x
\]

So, the result of distributing \(x\) is:
\[
x^3 + x^2 + 2x
\]

2. Now, distribute \(-9\) to each term in \(x^2 + x + 2\):
\[
-9 \cdot x^2 = -9x^2
\]
\[
-9 \cdot x = -9x
\]
\[
-9 \cdot 2 = -18
\]

So, the result of distributing \(-9\) is:
\[
-9x^2 - 9x - 18
\]

3. Now, combine all the terms from both distributions:
\[
x^3 + x^2 + 2x - 9x^2 - 9x - 18
\]

4. Combine like terms:
- \(x^2 - 9x^2 = -8x^2\)
- \(2x - 9x = -7x\)

So the expression simplifies to:
\[
x^3 - 8x^2 - 7x - 18
\]

Thus, the expanded expression in standard form is:
\[
\boxed{x^3 - 8x^2 - 7x - 18}
\]